In case of such vehicles, it may be required to also operate the vehicle heater when the drive motor and thus also the engine compartment is heated by a prior operation of the drive motor, especially when these vehicles are configured as so-called plug-in hybrids. Since the fuel line leading to the vehicle heater extends in at least some areas in the engine compartment and thus also comparatively close to the drive motor because of the positioning of the vehicle heater in the engine compartment, there is the risk in this state that the fuel generally flowing almost pressurelessly through the fuel line evaporates or forms bubbles. If such bubbles reach the combustion chamber during the combustion operation, this can lead to a flame-out or to a compromise of the combustion characteristics and thus to an increased emission of harmful substances.